I think it's arguable that she does. By doing what she does she relieves the system from taking care of her grandmother, and thereby making whatever small amount of taxpayer money usable for something else meanwhile taking that economic burden on herself.
(Edit: It can of course be seen that whatever wellfare money she gets is the equivalent of her service to grandmother/society, but in that case it's still at worst a zero sum scenario.)
I can imagine other fulfilling activities like helping less fortunate people get back on their feet, which could provide a giant boost to the economy but aren't really directly profitable (as the poor have no money)
Regardless, the grandma won't be doing in the street without BI, just like she isn't now. I'm not arguing against providing care for the elderly. I'm just saying that if a single individual chooses to spend her life caring for another single individual, maybe that person isn't performing a service to society. Maybe she's performing a service to her grandma, and nobody else.
And hence "society". Social costs and benefits (also known as "externalities") are simply costs and benefits to anyone outside of the decision to engage in a excahnge.
Why do you assume she couldn't be getting paid for it? Maybe she's just not charging.